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6. Magnetic Fields in Matter

6. Magnetic Fields in Matter. Matter becomes magnetized in a B field. Induced dipoles: Diamagnets. Permanent dipoles : Paramagnets Ferromagnets. Magnetic dipoles are different from electric dipoles. The dipoles are atomic current loops.

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6. Magnetic Fields in Matter

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  1. 6. Magnetic Fields in Matter Matter becomes magnetized in a B field. Induced dipoles: Diamagnets Permanent dipoles : Paramagnets Ferromagnets

  2. Magnetic dipoles are different from electric dipoles.

  3. The dipoles are atomic current loops. The angular momenta l and s are quantized, i. e. they take fixed values, so does m.

  4. Force on a magnetic dipole: Torque on a magnetic dipole (current loop):

  5. Derivation for the square loop gives the general result.

  6. Liquid oxygen is paramagnetic. Its dipoles are pulled into The inhomogeneous field of the permanent magnet.

  7. Paramagnetism The B field aligns the magnetic moment of the atoms/molecules. The thermal motion makes the orientation random. Competition results in partial alignment Magnetization Averaging over a small volume, which contains many atomic dipoles.

  8. The change has the opposite direction of B. Diamagnetism The dipole moments of all atomic orbitals change, because the orbital motion is changed. Much weaker than paramagnetism. Only important, if paramagnetism is zero.

  9. A superconductor is a perfect diamagnet. Here, the superconducting Pendelum bob is repelled by the permanent magnet.

  10. Field of a Magnetized Object We consider the macroscopic field, which is the average over a small volume containing many dipoles.

  11. Bound surface current Bound volume current

  12. Bound surface current Interpretation of the surface current

  13. Bound volume current Interpretation of the bound volume current

  14. Example 6.1 Field of the uniformly magnetized sphere.

  15. The free current is at our disposal, the bound current is generated by the material. Auxiliary field Ampere’s law The Auxiliary Field H Many other authors call H “magnetic field” and B “induction” or “flux density”.

  16. Magnetic susceptibility Permeability Permeability of free space Linear Media For paramagnets and diamagnets there are the linear relations

  17. Example 6.2

  18. Example 6.3 Solenoid filled with linear Material.

  19. Boundary conditions

  20. At surfaces between materials of different susceptibility:

  21. Ferromagnetism Unlike in paramagnetic material, there is a strong interaction between the spins of the atoms/molecules, which aligns them.

  22. The ferromagnet is composed of domains with different orientation of M. In the unmagnetizedstate they compensate each other.

  23. Domains in an Fe-3% Si crystal observed in a scanning electron microscope. The four colors indicate the four possible domain directions.

  24. In the presence of an external field the domains with an M that is similar to H grow. Saturation is reached when only the best domain survived.

  25. Hysteresis loop

  26. Magnetic field lines on a cobalt magnetic recording tape. The Solid arrows indicate the encoded magnetic bits.

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